The purpose of this work is to develop nonparametric hypothesis tests for use in general situations. The tests are developed using two statistical methods, permutation tests and likelihood-based score tests. The permutation tests are developed for censored data as well as for repeated measures data. We estimate a functional of the hyper-distributions of the treatment groups using U-statistic methods and estimated distribution functions for individuals. Several different types of tests may be formed depending on the choice of functional, motivated by the type of treatment difference we wish to highlight, or the choice of estimated distribution function, motivated by the type of data. When a Mann-Whitney functional is used with repeated measures data, we obtain a new rank invariant test analogous to an ANOVA test. When a difference in means functional is used with censored data, we obtain a new test which generalizes the permutation t-test to censored data. This new methodology is useful when standard assumptions (for example, proportional hazards or proportional odds) do not hold. One paper has been published on this methodology and one has been submitted. This work was done in collaboration with Dr. C. Gennings of the Medical College of Virginia and Dr. J. Shih of the National Heart, Lung, and Blood Institute. The score tests are developed for interval censored data. Interval censored data are data where the responses are not observed directly but are only known to reside in some interval. A paper has been published describing these new score tests and relating them to existing tests for interval censored data.